Donald Trump’s supreme court nominee, Brett Kavanaugh, and the woman accusing him of sexual assault have been invited to testify in an extraordinary public hearing that could determine the fate of his confirmation.

Under immense pressure, Chuck Grassley, the Republican chair of the Senate judiciary committee, said his panel would hold a hearing next Monday with both Kavanaugh and Christine Blasey Ford, who alleged that he sexually assaulted her when they were both teenagers in high school.

“To provide ample transparency, we will hold a public hearing Monday to give these recent allegations a full airing,” Grassley said in a written statement, as Republican leaders attempt to prevent the accusation from sinking Kavanaugh’s nomination.

Ford’s allegation, made in the Washington Post on Sunday, plunged Kavanaugh’s nomination into uncertainty, delaying a committee vote on his confirmation that had been scheduled for Thursday. But Republicans, including the Senate majority leader, Mitch McConnell, remained defiant that the process would move forward.

Trump said the nominee “looks forward to a hearing where he can clear his name of this false allegation” and stands ready to testify as soon as the panel calls him.

Trump defended Kavanaugh earlier on Monday, calling him “one of the finest people I’ve ever known” while saying he did not have a problem with delaying the vote.

“If it takes a little delay, it’ll take a little delay,” he told reporters. He added: “They’ll go through a process and hear everybody out. I think it’s important.”

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Asked if Kavanaugh had offered to withdraw his nomination, Trump did not answer directly, simply responding: “What a ridiculous question.”

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Lawyer for Brett Kavanaugh sexual assault accuser speaks out – video

Ford, 51, is a research psychologist at Palo Alto University in northern California. Speaking to the Post, she described an incident she said happened when she and Kavanaugh were in high school in the early 1980s.

She alleged that Kavanaugh and a friend – both “stumbling drunk” – corralled her into a bedroom at a party. Kavanaugh then pinned her on a bed, she said, groping her and placing his hand over her mouth. Ford said she was able to escape only when the friend jumped on top of them.

In a statement released by the White House on Monday, Kavanaugh issued a fresh denial of the claims: “I have never done anything like what the accuser describes – to her or to anyone.

“Because this never happened, I had no idea who was making this accusation until she identified herself yesterday. I am willing to talk to the Senate judiciary committee in any way the committee deems appropriate to refute this false allegation, from 36 years ago, and defend my integrity.”

Ford’s lawyer, Debra Katz, told NBC’s Today Show her client was “willing to do whatever it takes to get her story forth”.

Republicans hope to confirm Kavanaugh before the midterm elections in November, when their Senate majority could be at risk. But by midday a growing number of Republicans had sought to delay the vote until senators had more time to examine the claims.

Senator Jeff Flake, a Republican on the committee who called for the vote to be delayed, said a public hearing was the “best route forward”.

“Obviously these are serious charges, and if they’re true, I think that they’re disqualifying,” he told reporters.

Senator Orrin Hatch of Utah, a senior judiciary committee member and strong Republican supporter of Kavanaugh, said he spoke on Monday to Kavanaugh, who said he was not present at the party where the alleged assault occurred.

Hatch said: “I’ve known him for a long time, he’s always been straightforward, honest, truthful, and a very, very decent man.”

Democrats have called for the FBI to handle the matter by reopening Kavanaugh’s background investigation.

“Republicans and their staff cannot investigate these allegations,” the Senate minority leader, Charles Schumer, said in remarks on the Senate floor. “They’ve already said they’re not true.”

Republican leadership meanwhile fumed at Democrats for not previously disclosing this information, during their one-on-one meetings with Kavanaugh or during his confirmation hearing, which drew raucous protests and partisan bickering earlier this month.

“Now – at the 11th hour, with committee votes on the schedule, after Democrats have spent weeks and weeks searching for any possible reason that the nomination should be delayed,” McConnell said in remarks on the House floor.

Dianne Feinstein, the ranking Democrat, received a letter from Ford detailing the allegations in July, in which she asked for complete anonymity. In the interview with the Post, Ford said she decided to come forward publicly only after the allegations – and her identity – began to circulate.

Feinstein and nine other Democrats on the committee have signed a letter demanding that the matter be turned over to the FBI to investigate rather than have members’ staff make phone calls.

“In view of the enormity and seriousness of these allegations, a staff-only phone call behind closed doors is unacceptable and Democratic staff will not participate,” the letter said. “This isn’t how things should be done and is in complete violation of how this committee has worked in the past.”

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Brett Kavanaugh's confirmation hearing in three minutes – video

The allegations have raised the stakes for a handful of moderate Democratic senators and two Republican senators, Susan Collins of Maine and Lisa Murkowski of Alaska, all of whom were already undecided on Kavanaugh’s nomination.

On Monday, Collins wrote on Twitter: “Professor Ford and Judge Kavanaugh should both testify under oath before the Judiciary Committee.”

The White House has sought to cast Kavanaugh as a champion for women. As the Ford allegation surfaced late last week, initially anonymously, a pro-Kavanaugh letter was published, signed by 65 women who said he had always “behaved honorably and treated women with respect”.

The friend of Kavanaugh’s named in the Post report, the writer Mark Judge, said he had “no recollection” of the alleged events.

In an interview with Fox & Friends on Monday, White House counsellor Kellyanne Conway said it would be up to the Senate committee to decide if Ford speaks publicly or privately.

“Let me make this very clear,” she said. “I’ve spoken to the president. I’ve spoken to Senator Graham and others. This woman will be heard.”

Katz noted that her client had not wanted to come forward publicly and did so only after the accusations began to circulate late last week.

The Guardian separately obtained a letter that was sent to senators on the judiciary committee in July, in which a lawyer called for senators Grassley and Feinstein to offer whistleblower protection to a half dozen people who previously worked for Kavanaugh’s mentor and friend, Judge Alex Kozinski.

Kozinski resigned from his powerful post at the chief just of the ninth circuit last year after more than a dozen women accused him of sexual harassment and - in some cases – assault. Kozinski resigned and did not dispute the allegations, but said he had been misunderstood.

During his confirmation hearing last week, Kavanaugh said he had no knowledge of Kozinski’s allegedly abusive behaviour towards clerks. Former clerks for Kozinski have told the Guardian Kozinski’s behaviour was an “open secret”.